All Questions
Tagged with finite-geometry gr.group-theory
6 questions
16
votes
1
answer
395
views
Geometric interpretation of the exceptional isomorphism PSp(4,3)=PSU(4,22)
It is well-known that there is an isomorphism between PSp(4,3) (the symplectic group of dimension 4 over F3) and PSU(4,22) (the unitary group defined by 4×4 unitary matrices ...
4
votes
1
answer
186
views
Is there a unique Baer subplane in a finite Desarguesian projective plane?
An order-m subplane of a finite projective plane of order n is called a Baer subplane if n=m2.
It is known that the projective plane PG(2,q) is a Baer subplane of the Desarguesian ...
6
votes
1
answer
445
views
Kantor's Singer cycle theorem
I'm trying to understand the proof of Kantor's Singer cycle theorem, which asserts that if G is a subgroup of GL(n,q) containing a Singer cycle then $\operatorname{GL}(n/s,q^s) \leq ...
2
votes
1
answer
183
views
Is inner product preserved only by the stabiliser in a finite reflection group?
Is the following statement true for finite reflection groups?
Let G be a finite reflection group acting on Rn, let x,y∈Rn
and let z be in the orbit of y. If $\...
3
votes
0
answers
195
views
Vector spaces over a field of prime order with certain hyperplanes
Let V be a vector space of finite dimentional d over a field of prime order p.
For what values of d and p, one can find d+1 (pairwise distinct) hyperplanes (subspaces of dimension d−1) $...
14
votes
0
answers
552
views
Who conjectured that a transitive projective plane is Desarguesian?
The only known finite projective plane with a transitive automorphism group is the Desarguesian plane PG(2,q) and it seems likely that there are no others, although this is not (quite) proved.
...